Session A29: Focus Session: Carbon Nanotubes and Related Materials I: Graphene Transport

Thermopower of Few-Layer Graphene Devices

We report thermopower measurements of few-layer graphene (FLG) devices at low temperatures. FLG flakes are separated by mechanical exfoliation and then connected to form devices using electron beam lithography. FLG devices are fabricated on a 300 nm-thick SiO2 layer which separates from the heavily-doped silicon substrate used as a gate. As the gate voltage is swept from -55 V to 55 V, the electrical conductivity of FLG devices undergoes a minimum. In the meantime, the Seebeck coefficient changes the sign near the conductivity minimum, marking the transition from p- to n-type in graphene. By directly comparing the derivative of the logarithmic conductivity with the measured Seebeck coefficient, we have experimentally validated the Mott relation. We have also measured the Seebeck coefficient and electrical conductivity under magnetic fields up to 8T. Detailed analysis of the experimental data will be presented.   

Measurement of the Thermal Conductance at the Graphene-Quartz Interface by Optical Pump-Probe Spectroscopy

We have determined the interfacial thermal conductance of single and multi-layer graphene samples prepared on quartz substrates by mechanical exfoliation of graphite. The measurements were performed by suddenly heating the graphene sample with a femtosecond optical laser pulse and then monitoring the sample's subsequent temperature evolution through the slight changes in reflectivity experienced by a time-delayed optical probe pulse. For the study of thermal transport, the transient response occurring on a time scale of tens of picoseconds was relevant. A faster transient related to non-equilibrium electronic excitation was also observed at early delay times. By studying the dependence of the slow decay component on the number of graphene layers in the sample, we could identify interfacial heat flow as the relaxation mechanism. An interfacial conductance in excess of 5,000W/cm$^{2}$K was deduced for the graphene-quartz system which is in the same order of magnitude compared to similar measurements on carbon nanotube suspensions [Huxtable et al. Nature Materials 2003].   

A graphene-based atomic-scale switch

Graphene's remarkable mechanical and electrical properties combined with its compatibility with existing planar CMOS technology make it an attractive material for novel computing devices. Thus far work has focused primarily on realizing transistor functionality. To complement this effort, we have developed a graphene-based switch that realizes a non-volatile memory element. Our devices have demonstrated tens of thousands of writing cycles and long retention times. Additionally, the devices' atomic-scale dimensions correspond to bit densities far greater than present-day memory technologies. We will present the fabrication process, switching behavior, and further performance characterization.   

Electronic properties of graphene

Graphene is a first two-dimensional atomic crystal. In my talk I'll overview our latest results on the electronic properties of this material.   

Charged Impurity Scattering in Graphene

We have measured the impact of charged impurity scattering on the transport properties of graphene sheets [1]. We vary the density of adsorbed potassium atoms in our experiment up to $5 \times 10^{12} K/cm^2$ on the surface of graphene based-devices which are otherwise devoid of any surface adsorbates [2] in ultra high vacuum environment. Adsorbed potassium decreases the charge carrier mobility, renders the gate-dependent conductivity linear, shifts the minimum conductivity point in gate voltage, broadens the width of minimum conductivity region, and lowers the minimum conductivity. Our results are in qualitative agreement with a recent Boltzmann transport calculation [3]. New features, such as asymmetric response of electron-hole mobility and the observation of a ``residual'' conductivity (the extrapolation of the linear gate-voltage dependent conductivity to the minimum conductivity point) near 2 $e^2/h$, indicate transport properties beyond the simple Boltzmann picture. [1] J.H.Chen et al., http://xxx.lanl.gov/abs/0708.2408. [2] M.Ishigami et al., Nano Letters, 7, 1643 (2007). [3] S. Adam et al., PNAS 104, 18392 (2007).   

Conductivity and Fano factor in disordered graphene

Using the recursive Green's function method, we study the problem of electron transport in a disordered single-layer graphene sheet. The conductivity is of order $e^2/h$ and its dependence on the carrier density has a scaling form that is controlled solely by the disorder strength and the ratio between the sample size and the correlation length of the disorder potential. The shot noise Fano factor is shown to have a narrow dip near the neutrality point for weak disorder and to develop a nearly doping independent behavior at strong disorder. Our results are in good qualitative and quantitative agreement with experiments and provide a way for extracting microscopic information about the magnitude of extrinsic disorder in graphene.   

The conductivity of pure graphene

Pure graphene, in the absence of impurities or bias voltage, is described by a theory of Dirac fermions with Coulomb interactions. We argue that this theory has a finite conductivity, $\sigma$, and show that at frequencies $\omega \ll k_B T/\hbar$ (where $T$ is absolute temperature) $\sigma = \Xi (e^2/h) (\ln (W/T))^2 $, where $W$ is the bandwidth, and $\Xi$ is a {\em universal} number. We compute $\Xi$ by the solution of a quantum Boltzmann equation. The influence of a dilute concentration of impurities and finite bias voltage is also discussed.   

Theoretical study of graphene transport regimes

In recent work [Adam et al. Proc. Natl. Acad. Sci. 104, 18392 (2007); Y.-W. Tan et al. arXiv:0707.1807, Phys. Rev. Lett., in press (2007)], we argued that the transport properties of currently available experimental graphene samples are dominated by diffusive carriers scattering off Coulomb impurity centers typically located in the substrate. In the current paper we study graphene monolayers, bilayers and nanoribbons and show theoretically that by tuning external parameters, one can access several different transport regimes ranging from the aforementioned diffusive Boltzmann transport to phase-coherent ballistic transport to classical percolation through puddles of electrons and holes. This work is supported by U.S. ONR and NRI-NSF.   

Impact of physisorbed species on transport properties of graphene

We have measured the impact of physisorbed species, including Argon, Krypton, Nitrogen, water and Benzene, on the transport properties of mechanically-exfoliated graphene sheets on SiO$_{2}$/Si in an ultra-high vacuum environment at temperatures near 30 K. We controlled the gas dosage down to the sub-monolayer level and found species-specific effects on the field-effect mobility of graphene. We observed the influence of different molecular sizes, molecular dipole moment, and intermolecular interactions. We will discuss our results in the context of recent theoretical calculations within the Boltzmann transport framework.   

Stress-induced Controlled Fabrication of Graphene Nano Ribbons and Carbon Nanotubes via Electrostatic force and electrical transport properties of freely suspended graphene monolayers and bi-layers.

A simple electrostatic technique to transfer loosely bound graphene sheets from a freshly cleaved highly oriented pyrolitic graphite (HOPG) to a desired substrate has been recently reported (Sidorov \textit{et al}., Nanotechnology, 2007). Here we demonstrate that this technique can be further extended to roll/scroll graphene sheets in a controllable manner by changing the environment during this electrostatic deposition. Deposition under high vacuum (10$^{-7}$ Torr) is observed to deposit extremely flat graphene monolayers on a substrate. In contrast, high density of completely scrolled graphene layers are observed in hydrogen atmosphere and in the presence of an electrostatic field. No scrolling was seen in He atmosphere; but partial scrolling is seen in nitrogen atmosphere under the influence of an electrostatic force. It is believed that in addition to the stress induced due to the adsorption of hydrogen, an additional electrostatic field is necessary to scroll the graphene layers loosely bound to HOPG. Also electrical transport properties of monolayers and bi-layers of graphene layers freely suspended between two electrodes and deposited between trenches on a substrate will be presented and compared.   

Interaction of Si atoms and Si-based radicals with carbon nanotubes and graphene monolayers

We use {\em ab initio} density functional calculations to study the interaction of Si atoms and Si-based radicals, such as SiH$_3$, with single-wall carbon nanotubes and graphene monolayers. We find that both Si atoms and radicals form a strong chemisorption bond, accompanied by a small relaxation and a locally increased sp$^3$ bond character of the graphitic nanostructure. We identify the optimum adsorption geometries at different adsorbate coverages and adsorbate-related changes in the electronic structure and vibration spectra of the systems. We propose that successful functionalization of carbon nanotubes or graphene by Si atoms or Si-based radicals can be verified by studying changes in the radial breathing mode of nanotubes and the G-band of graphitic nanocarbons using Raman spectroscopy.   

First-principles Studies of Metal Adsorption on Graphene

Quantitative first-principles theory can aid in understanding many experimental phenomena involving metal adsorption on graphene and carbon nanotubes, including adatom mass transport, modification of electronic, mechanical, and magnetic properties, and adhesion and efficacy of electrical contacts. In this work, the binding energy and geometry, charge transfer, work function, and electronic structure of adatom-graphene systems are calculated using first-principles density functional theory for a variety of metal elements. Trends in these calculated data are analyzed, and their implications for graphene-based devices are discussed.   

Carbon-based ion and molecular channels

We design ion and molecular channels based on layered carboneous materials, with chemically-functionalized pore entrances. Our molecular dynamics simulations demonstrate that these ultra-narrow pores, with diameters around 1 nm, are highly selective to the charges and sizes of the passing (Na$^{+}$ and Cl$^{-})$ ions and short alkanes. We demonstrate that the molecular flows through these pores can be easily controlled by electrical and mechanical means. These artificial pores could be integrated in fluidic nanodevices and lab-on-a-chip techniques with numerous potential applications. [1] Kyaw Sint, Boyang Wang and Petr Kral, submitted. [2] Boyang Wang and Petr Kral, JACS 128, 15984 (2006).